Collaborative Filtering with Smooth Reconstruction of the Preference Function

The problem of predicting the rating of a set of users to a set of items in a recommender system based on partial knowledge of the ratings is widely known as collaborative filtering. In this paper, we consider a mapping of the items into a vector space and study the prediction problem by assuming an underlying smooth preference function for each user, the quantization at each given vector yields the associated rating. To estimate the preference functions, we implicitly cluster the users with similar ratings to form dominant types. Next, we associate each dominant type with a smooth preference function; i.e., the function values for items with nearby vectors shall be close to each other. The latter is accomplished by a rich representation learning in a so-called frequency domain. In this framework, we propose two approaches for learning user and item representations. First, we use an alternating optimization method in the spirit of $k$-means to cluster users and map items. We further make this approach less prone to overfitting by a boosting technique. Second, we present a feedforward neural network architecture consisting of interpretable layers which implicitely clusters the users. The performance of the method is evaluated on two benchmark datasets (ML-100k and ML-1M). Albeit the method benefits from simplicity, it shows a remarkable performance and opens a venue for future research. All codes are publicly available on the GitLab.